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A265318 Fibonacci word fractal in an n X n grid, starting downwards from the top-left corner, listed antidiagonally.

%I A265318 #17 Dec 24 2024 12:49:09
%S A265318 1,0,2,5,3,0,6,4,0,0,7,0,0,0,0,0,8,10,0,0,20,0,0,9,11,0,19,21,0,0,0,0,
%T A265318 12,18,0,22,0,0,0,0,13,0,17,23,0,0,0,0,0,0,14,16,0,24,26,0,0,0,0,0,0,
%U A265318 15,0,0,25,27,0,0,0,0,0,0,0,0,0,0,0,28,83
%N A265318 Fibonacci word fractal in an n X n grid, starting downwards from the top-left corner, listed antidiagonally.
%C A265318 The n-th iteration of this curve ends at the n-th Fibonacci number.
%C A265318 As this is not a space-filling curve, not all points on the grid are reached by the curve; these points are given the value 0.
%H A265318 Max Barrentine, <a href="/A265318/b265318.txt">Table of n, a(n) for n = 1..2484</a>
%H A265318 Alexis Monnerot-Dumaine, <a href="https://hal.archives-ouvertes.fr/hal-00367972">The Fibonacci Word fractal</a>, HAL Id: hal-00367972, 2009.
%H A265318 Alexis Monnerot-Dumaine, <a href="/A171587/a171587.pdf">The Fibonacci word fractal</a> [Cached copy, with permission]
%e A265318 The top left corner of the array shows how this curve begins (connect the terms in numerical order):
%e A265318    1   0   5   6   7
%e A265318    2   3   4   0   8
%e A265318    0   0   0  10   9
%e A265318    0   0   0  11   0
%e A265318    0   0   0  12  13
%e A265318   20  19  18   0  14
%e A265318   21   0  17  16  15
%e A265318   22  23   0   0   0
%e A265318    0  24   0   0   0
%e A265318   26  25   0   0   0
%e A265318   27   0  31  32  33
%e A265318   28  29  30   0  34
%Y A265318 Cf. A332298, A332299.
%Y A265318 See also A163357, A163334, and A054238 for other fractal curves.
%K A265318 nonn,tabl
%O A265318 1,3
%A A265318 _Max Barrentine_, Dec 06 2015